Problem: Alice has a cute cat. To keep her cat fit, Alice wants to design an exercising walk for her cat! 

Initially, Alice's cat is located in a cell (x,y) of an infinite grid. According to Alice's theory, cat needs to move: 

  * exactly a steps left: from (u,v) to (u-1,v); 
  * exactly b steps right: from (u,v) to (u+1,v); 
  * exactly c steps down: from (u,v) to (u,v-1); 
  * exactly d steps up: from (u,v) to (u,v+1). 



Note that the moves can be performed in an arbitrary order. For example, if the cat has to move 1 step left, 3 steps right and 2 steps down, then the walk right, down, left, right, right, down is valid.

Alice, however, is worrying that her cat might get lost if it moves far away from her. So she hopes that her cat is always in the area [x_1,x_2]× [y_1,y_2], i.e. for every cat's position (u,v) of a walk x_1 ≤ u ≤ x_2 and y_1 ≤ v ≤ y_2 holds.

Also, note that the cat can visit the same cell multiple times.

Can you help Alice find out if there exists a walk satisfying her wishes?

Formally, the walk should contain exactly a+b+c+d unit moves (a to the left, b to the right, c to the down, d to the up). Alice can do the moves in any order. Her current position (u, v) should always satisfy the constraints: x_1 ≤ u ≤ x_2, y_1 ≤ v ≤ y_2. The staring point is (x, y).

You are required to answer t test cases independently.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^3) — the number of testcases. 

The first line of each test case contains four integers a, b, c, d (0 ≤ a,b,c,d ≤ 10^8, a+b+c+d ≥ 1).

The second line of the test case contains six integers x, y, x_1, y_1, x_2, y_2 (-10^8 ≤ x_1≤ x ≤ x_2 ≤ 10^8, -10^8 ≤ y_1 ≤ y ≤ y_2 ≤ 10^8).

Output

For each test case, output "YES" in a separate line, if there exists a walk satisfying her wishes. Otherwise, output "NO" in a separate line. 

You can print each letter in any case (upper or lower).

Example

Input


6
3 2 2 2
0 0 -2 -2 2 2
3 1 4 1
0 0 -1 -1 1 1
1 1 1 1
1 1 1 1 1 1
0 0 0 1
0 0 0 0 0 1
5 1 1 1
0 0 -100 -100 0 100
1 1 5 1
0 0 -100 -100 100 0


Output


Yes
No
No
Yes
Yes
Yes

Note

In the first test case, one valid exercising walk is $$$(0,0)→ (-1,0) → (-2,0)→ (-2,1) → (-2,2)→ (-1,2)→(0,2)→ (0,1)→ (0,0) → (-1,0)$$$

Solution (in JAVA):

Solution:
//package codeforces;
import java.util.*;
import java.io.*;
import javafx.util.Pair;

public class esehi {
  static FastReader scan;
  static PrintWriter pw;
  static int count = 0;

  public static void main(String[] args) {

    new Thread(null, null, "Thread 1", 1 << 27) {
      public void run() {
        try {
          setup();
          solve();
          closeResources();
        } catch (Exception e) {
          e.printStackTrace();
          System.exit(1);
        }
      }
    }.start();
  }

  private static void solve() throws IOException{
    int t = ni();
    while(t-- > 0) {
      long a = nl();
      long b = nl();
      long c = nl();
      long d = nl();
      long x = nl();
      long y = nl();
      long x1 = nl();
      long y1 = nl();
      long x2 = nl();
      long y2 = nl();

      x -= a-b;
      y -= c-d;
      if(a+b > 0 && x1==x2) pl("NO");
      else if( c+d > 0 && y1==y2) pl("NO");
      else if((x >= x1 && x <= x2)&&(y >= y1 && y <= y2)) pl("YES");
      else pl("NO");

    }
  }

  static String ns() throws IOException {
    return scan.readString();
  }


  static int ni() throws IOException {
    return scan.ni();
  }

  static long nl() throws IOException {
    return scan.nl();
  }

  static long[] nla(int n) throws IOException {
    long []data = new long[n];
    for (int i = 0; i < n; i++) {
      data[i] = nl();
    }
    return data;
  }

  static int[] nia(int n) throws IOException {
    int []data = new int[n];
    for (int i = 0; i < n; i++) {
      data[i] = ni();
    }
    return data;
  }

  static void pl() {
    pw.println();
  }

  static void p(Object o) {
    pw.print(o + " ");
  }

  static void pl(Object o) {
    pw.println(o);
  }

  static void psb(StringBuilder sb) {
    pw.print(sb);
  }

  static void pa(Object arr[]) {
    for (Object o : arr) {
      p(o);
    }
    pl();
  }

  static void pa(int arr[]) {
    for (int o : arr) {
      p(o);
    }
    pl();
  }

  static void pa(long arr[]) {
    for (long o : arr) {
      p(o);
    }
    pl();
  }

  static void pa(double arr[]) {
    for (double o : arr) {
      p(o);
    }
    pl();
  }

  static void pa(char arr[]) {
    for (char o : arr) {
      p(o);
    }
    pl();
  }

  static void pa(List list) {
    for (Object o : list) {
      p(o);
    }
    pl();
  }

  static void pa(Object[][] arr) {
    for (int i = 0; i < arr.length; ++i) {
      for (Object o : arr[i]) {
        p(o);
      }
      pl();
    }
  }

  static void pa(int[][] arr) {
    for (int i = 0; i < arr.length; ++i) {
      for (int o : arr[i]) {
        p(o);
      }
      pl();
    }
  }

  static void pa(long[][] arr) {
    for (int i = 0; i < arr.length; ++i) {
      for (long o : arr[i]) {
        p(o);
      }
      pl();
    }
  }

  static void pa( char[][] arr) {
    for (int i = 0; i < arr.length; ++i) {
      for (char o : arr[i]) {
        p(o);
      }
      pl();
    }
  }

  static void pa(double[][] arr) {
    for (int i = 0; i < arr.length; ++i) {
      for (double o : arr[i]) {
        p(o);
      }
      pl();
    }
  }

  static class FastReader {
    private final InputStream stream;
    private final byte[] buf = new byte[8192];
    private int curChar, snumChars;

    public FastReader(InputStream stream) {
      this.stream = stream;
    }

    public int read() {
      if (snumChars == -1)
        throw new InputMismatchException();
      if (curChar >= snumChars) {
        curChar = 0;
        try {
          snumChars = stream.read(buf);
        } catch (IOException e) {
          throw new InputMismatchException();
        }
        if (snumChars <= 0)
          return -1;
      }
      return buf[curChar++];
    }

    public int ni() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      int sgn = 1;
      if (c == '-') {
        sgn = -1;
        c = read();
      }
      int res = 0;
      do {
        res *= 10;
        res += c - '0';
        c = read();
      } while (!isSpaceChar(c));
      return res * sgn;
    }

    public long nl() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      int sgn = 1;
      if (c == '-') {
        sgn = -1;
        c = read();
      }
      long res = 0;
      do {
        res *= 10;
        res += c - '0';
        c = read();
      } while (!isSpaceChar(c));
      return res * sgn;
    }

    public int[] nextIntArray(int n) {
      int a[] = new int[n];
      for (int i = 0; i < n; i++) {
        a[i] = ni();
      }
      return a;
    }

    public String readString() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      StringBuilder res = new StringBuilder();
      do {
        res.appendCodePoint(c);
        c = read();
      } while (!isSpaceChar(c));
      return res.toString();
    }

    public String nextLine() {
      int c = read();
      while (isSpaceChar(c))
        c = read();
      StringBuilder res = new StringBuilder();
      do {
        res.appendCodePoint(c);
        c = read();
      } while (!isEndOfLine(c));
      return res.toString();
    }

    public boolean isSpaceChar(int c) {
      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    private boolean isEndOfLine(int c) {
      return c == '\n' || c == '\r' || c == -1;
    }

    public void close() throws IOException {
      if (stream == null) {
        return;
      }
      stream.close();
    }
  }

  private static void setup() {
    scan = new FastReader(System.in);
    pw = new PrintWriter(System.out, true); // set auto flush to true if you want to directly flush to the output stream.
  }

  private static void closeResources() throws IOException {
    pw.flush();
    pw.close();
    scan.close();
  }

}